I have a 2002 WRX wagon with the 4EAT automatic transmission.
The problem I have is only during cold weather (32 deg F) after sitting all night. I'll take off from my drive way in the morning, going uphill, and try to accelerate hard to match the speed of possible traffic on a rural highway.
The car engine sounds like it's spinning fast, and the tach shows the RPM rising past 4000. Meanwhile the car is slowly accelerating to about 10 to 15 mph. Scary, the way people drive on that road.
Eventually, after driving 10 minutes or so the problem goes away. This doesn't happen on warm days.
I was thinking that the problem was in the torque converter linkage. I would think that the gearing itself would make some sort of grinding sound if the gears were only partially meshing. What do people think? I have 90000 mi on the WRX and would love to find something for the dealer to fix NOW, before the warranty runs out at 100000 mi.
Slipping when it is cold often means that the line pressure is lower than it should be and that can be a result of fluid which is too viscous or has not been changed recently, plugged filter, dirty valve body parts, deteriorated rings or seals, and a worn pump.
When I took some transmission classes years ago, the instructor said always suspect the front pump when this sort of behavior was noticed. But, as Steve posted, other things can affect it too.
Have you serviced it recently? A service and adjust (if it is one that has adjustable bands) might be money well spent.